Modeling functional data with spatially heterogeneous shape characteristics.

Area of Science:

• Statistics
• Biostatistics
• Medical Imaging Analysis

Background:

• Functional data analysis often requires modeling complex marginal distributions and dependence structures.
• Skewness and heavy tails in data can vary across spatial or temporal locations, posing analytical challenges.
• Existing methods may not adequately capture these location-specific distributional characteristics.

Purpose of the Study:

• To develop a novel class of statistical models for functional data with location-dependent skewness and shape characteristics.
• To provide a computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions.
• To apply these methods to identify disease-affected regions in neuronal tracts from medical imaging studies.

Main Methods:

• Utilizing copula-based models to independently specify marginal distributions and dependence structures.
• Modeling marginal distributions using the skew t family, with location-dependent mean, variance, and shape parameters.
• Employing Gaussian or t-copulas to capture the underlying latent Gaussian process for dependence structure.

Main Results:

• A novel inferential framework was developed for estimating complex marginal distributions.
• The methods successfully identified specific locations along neuronal tracts most affected by multiple sclerosis.
• Demonstrated the utility of the models in a real-world medical study.

Conclusions:

• The proposed models offer a flexible and powerful approach for analyzing functional data with varying distributional properties.
• This framework provides new tools for complex data analysis in medical and public health research.
• The methodology has broad applicability to various functional data sets, including higher-dimensional biological data like MRI.